2r+9/r=30

Solution for 2r+9/r=30 equation:

2r+9/r=30

We move all terms to the left:

2r+9/r-(30)=0


Domain of the equation: r!=0

r∈R


We multiply all the terms by the denominator


2r*r-30*r+9=0

We add all the numbers together, and all the variables

-30r+2r*r+9=0

Wy multiply elements

2r^2-30r+9=0

a = 2; b = -30; c = +9;
Δ = b2-4ac
Δ = -302-4·2·9
Δ = 828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{23}}{2*2}=\frac{30-6\sqrt{23}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{23}}{2*2}=\frac{30+6\sqrt{23}}{4}
$